The connections between an umbrella cover and struts in a prior art are principally by stitching the umbrella cover to ends and joints of struts so that the umbrella cover can cling to struts as opening or closing the umbrella, resulting in a nice-looking appearance and convenience of storage. However, the sewing method, largely depending on manpower, takes so much time and money that it seems to be not economical and impractical for production in a country that is thirsty for laborers. Furthermore, for an umbrella cover made of a single cloth that does not have tacks for stitching or PVC cloth that lacks of strength for stitching, stitching is not a feasible method for the production of folding umbrellas having such covers. Consequently, so far there are not on the market folding umbrellas that use a single cloth or PVC cloth as umbrella covers.